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Solutions for Physics, Class 8, ICSE
Assertion (A) : In order to come to surface of water, whales fill their swim bladder with water.
Reason (R) : A body floats when the density of the body is less than the density of the liquid.
Assertion is false but reason is true
Explanation
Assertion (A) is false because in order to come to the surface of water, whales fill the bladder with air to decreases the average density of the whale and so it rises to the surface.
Reason (R) is true because a body of density greater than the density of liquid, sinks inside the liquid, while a body of density equal or less than the density of liquid, floats on the liquid.
Fill in the blanks:
(a) 1 kg is the mass of ............... mL of water at 4°C.
(b) Mass = density x ............... .
(c) The S.I. unit of density is ............... .
(d) Density of water is ............... kg m-3.
(e) 1 g cm-3 = ............... kg m-3.
(f) The density of a body which sinks in water is ............... than 1000 kg m-3.
(g) A body sinks in a liquid A, but floats in a liquid B. The density of liquid A is ............... than the density of liquid B.
(h) A body X sinks in water, but a body Y floats on water. The density of the body X is ............... than the density of body Y.
(i) The buoyant force experienced by a body when floating in salt-water is ............... that when floating in pure water.
(j) The apparent weight of a body floating in a liquid is ............... .
(a) 1 kg is the mass of 1000 mL of water at 4°C.
(b) Mass = density x volume.
(c) The S.I. unit of density is kg m-3.
(d) Density of water is 1000 kg m-3.
(e) 1 g cm-3 = 1000 kg m-3.
(f) The density of a body which sinks in water is more than 1000 kg m-3.
(g) A body sinks in a liquid A, but floats in a liquid B. The density of liquid A is less than the density of liquid B.
(h) A body X sinks in water, but a body Y floats on water. The density of the body X is more than the density of body Y.
(i) The buoyant force experienced by a body when floating in salt-water is equal to that when floating in pure water.
(j) The apparent weight of a body floating in a liquid is zero.
The density of the material of a coin is determined by the following experiment:
The density of a liquid is determined by first finding its mass and then its volume.
A density bottle is a specially designed bottle which is used to determine the density of a liquid. The figure of density bottle is shown below:
Determination of Density of a Liquid using the Density Bottle
Sl. No. | Density | Relative Density |
---|---|---|
(i) | Density of a substance is defined as the mass of a unit volume of that substance. | The relative density of a substance is defined as the ratio of the density of a substance to the density of water. |
(ii) | Units are kg m-3, g cm-3. | Relative Density has no units. |
If the density of a body is less than the density of liquid, the body will float on the surface of the liquid. But if the density of a body is more than the density of liquid the body will sink in the liquid.
An iron needle is solid and density of iron is more than that of water. Weight of iron needle is more than the buoyant force of water on it so it sinks in water. Although ship is made of iron but it has hollow space that is filled with air which make its average density less than that of water, so ship floats on water.
Sea water contains salts so its density is more than the density of river water. The weight of a person gets balanced by the less immersed part of his body in sea water as compared to that in river water. Thus, it is easier to swim in sea water than in river water.
Density of ice (0.9 g cm-3) is less than the density of sea water (1.02 g cm-3). So, an iceberg floats in sea water with its large portion submerged inside the water and only a little portion of it is above the surface of water. Thus, a ship can collide with the invisible part of the iceberg under the surface of water. Hence, it is dangerous.
When a stone is under water then its weight is less than its weight in air because it experiences an upward buoyant force. Due to apparent loss in weight, it is lighter in water which makes it easier to lift in water than in the air.
A submarine is a water tight boat which can travel under water like a ship and it is provided with water tanks.
To make the submarine dive, the tanks are filled with water so that the average density of the submarine becomes greater than the density of sea water, so it sinks into the water.
To make the submarine rise to the surface of water, these tanks are emptied. This makes the average density of the submarine less than the density of sea water, so the submarine rises up to the surface of water.
The density of hydrogen gas is less than the density of air. So the buoyant force experienced by the balloon due to air is greater than the weight of the balloon. Due to this net upward force balloon rises up in air.
Column A | Column B |
---|---|
(a) kg m-3 | (iv) density |
(b) No unit | (i) relative density |
(c) Relative density | (v) density bottle |
(d) Iron | (ii) sinks in alcohol |
(e) Wood | (iii) floats on water |
(a) The density of air is 1.28 g litre-1.
1 litre = 1000 cm3
∴ Density of air in g cm-3 =
Density of air = 0.00128 g cm-3
(b) Density of air in kg m-3 = Density of air in g cm -3 x 1000 = 0.00128 x 1000 = 1.28 kg m-3
∴ Density of air in kg m-3 = 1.28 kg m-3.
Mass of wood = 150 g
Volume of wood = 200 cm3
Density of wood = ?
(a) C.G.S. unit of density is g cm-3.
Density of wood = 0.75 g cm-3.
(b) S.I. unit of density is kg m-3.
Density of Wood in kg m-3 = Density of Wood in g cm-3 x 1000 = 0.75 x 1000 = 750 kg m-3
So, Density of Wood = 750 kg m-3.
Mass of solid = 72 g
Volume of solid = Final volume of water - Initial volume of water
Volume of solid = 42 - 24 = 18 mL
So, Density of solid = 4.0 g cm-3.
Mass of empty density bottle (M1) = 21.8 g
Mass of bottle with water (M2) = 41.8 g
Mass of bottle with liquid (M3)= 40.6 g
(a) Mass of water in bottle = M2 - M1 = 41.8 - 21.8 = 20 g
Density of water is 1 g cm-3, so volume of density bottle = 20 mL
(b) Mass of liquid in bottle = M3 - M1 = 40.6 - 21.8 = 18.8 g
Relative density of liquid = 0.94.
Mass of empty density bottle (M1) = 22 g
Mass of bottle + water (M2) = 50 g
Mass of bottle + brine solution (M3) = 54 g
Mass of water in bottle = M2 - M1 = 50 - 22 = 28 g
Density of water is 1 g cm-3, so volume of density bottle = 28 cm3.
Mass of brine solution in bottle = M3 - M1 = 54 - 22 = 32 g
So, density of brine solution = 1.14 g cm-3.
So, Relative density of brine solution is 1.14.
Mass of empty density bottle (M1) = 30 g
Mass of bottle with water (M2) = 75 g
Mass of bottle with liquid (M3)= 65 g
(a) Mass of water in bottle = M2 - M1 = 75 - 30 = 45 g
Density of water is 1 g cm-3, so volume of density bottle = 45 mL.
(b) Mass of liquid in bottle = M3 - M1 = 65 - 30 = 35 g
So, density of liquid = 0.77 g cm-3.
(c)
So, Relative density of liquid is 0.77.
The density of aluminium is 2.7 g cm-3 and that of brass is 8.4 g cm-3. The correct statement is:
The mass of a certain volume of brass is more than the mass of equal volume of aluminium.
Reason —
So mass of certain volume of brass will be more than the mass of same volume of aluminium as density of brass is more than density of aluminium.
A density bottle has a marking 25 mL on it. It means that:
The density bottle will store 25 mL of any liquid in it.
Reason — A density bottle can store specific volume of any density of liquid. Since this bottle is marked 25 mL so it can store 25 mL of any density liquid in it.
The correct statement is:
The buoyant force on a body is equal to the weight of the liquid displaced by it.
Reason — According to Principle of Floatation, the buoyant force is equal to the weight of the liquid displaced by the immersed part of the body.
equal to the weight of the wood piece
Reason — According to Law of Floatation when a body floats on water the weight of the body is equal to the buoyant force.
sink
Reason — According to the Principle of Floatation, if the weight of the body is more than the buoyant force acting on the body the body will sink into the liquid.
When temperature increases, volume of most of the liquid increases, so density decreases. Similarly when temperature decreases volume of liquids decreases so density increases. But exception is water which contracts on heating from 0°C to 4°C and expands on heating above 4°C. Water has maximum density at 4°C.
(a) Mass of the liquid remains unaffected on heating.
(b) Volume of the liquid increases with increase in temperature.
(c) Density of liquid decreases on heating because its volume increases and density is inversely proportional to volume.
The law of floatation states that — "When a body floats in a liquid, the weight of the liquid displaced by its immersed part is equal to the total weight of the body".
i.e., while floating
Weight of the floating body = Weight of the liquid displaced by its immersed part (i.e., buoyant force)
The density of cork is less than the density of water so it floats on water surface but the density of iron nail is more than the density of water so it sinks in water.
(a) Iron will sink in water as density of iron (7.8 g cm-3) is more than the density of water (1 g cm-3).
(b) Iron will float in mercury as the density of iron (7.8 g cm-3) is less than the density of mercury (13.6 g cm-3).
(a) The buoyant force is same in each case as the weight of the body is same in each case and the buoyant force is equal to the weight of the liquid displaced by the immersed part of the body which balances the weight of the body.
(b) Liquid A has the least density as the maximum part of the body is immersed in liquid A.
(c) Liquid C has the highest density as the body immerses the least in liquid C.
The egg sinks in fresh water because the density of the egg is greater than the density of fresh water. However, when salt is added to water, the density of the solution increases. In a strong salt solution, the density becomes greater than that of the egg, so the upward buoyant force becomes strong enough to support the egg, causing it to float.
Sea water is denser than river water because it contains dissolved salts. When the ship is in sea water, the buoyant force acting on it is greater due to the higher density. As the ship moves to river water, where the density is lower, the buoyant force decreases. To balance its weight, the ship must displace more water, causing it to submerge deeper in river water.
All three pieces—the disc, the square, and the L-section—have exactly the same density.
Density is an intrinsic property of a material. For a given substance (here, iron) it depends only on the material's nature, not on the object's shape or size. Since each piece is cut from the same sheet of iron, their density remains the constant density of iron, regardless of how that mass is distributed geometrically.
Write true or false for each statement:
(a) Equal volumes of two different substances have equal masses.
(b) The density of a piece of brass will change by changing its size or shape.
(c) The density of a liquid decreases with increase in its temperature.
(d) Relative density of water is 1.0.
(e) Relative density of a substance is expressed in g cm-3.
(f) When a body is immersed in a liquid, the buoyant force experienced by the body is equal to the volume of the liquid displaced by it.
(g) If a body floats in different liquids, different volumes of the body get submerged in different liquids, but in each liquid the weight of the liquid displaced by the submerged part of body remain the same.
(h) A body experiences the same buoyant force when it floats or sinks in water.
(i) A body floats in a liquid when its weight becomes equal to the weight of the liquid displaced by its submerged part.
(j) A body while floating, sinks deeper in a liquid of low density than in a liquid of high density.
(a) False
Correct Statement — Equal volumes of two different substances have different masses.
(b) False
Correct Statement — The density of a piece of brass will not change by changing its size or shape.
(c) True
(d) True
(e) False
Correct Statement — Relative density has no unit.
(f) False
Correct Statement — When a body is immersed in a liquid, the buoyant force experienced by the body is equal to the weight of the liquid displaced by the immersed part of the body.
(g) True
(h) False
Correct Statement — The buoyant force experience by the body is different when floating or sinking in water.
(i) True
(j) True